Calcualate the molarity and molality of 20% aqueous ehtanol `(C_(2) H_(5) OH)` solution by volume. (density of solution `= 0.96 g mL^(-1)`)

Explanation

To calculate the molarity and molality of a 20% aqueous ethanol solution, we will follow these steps:

### Step 1: Understand the Given Information
- The solution is 20% ethanol by volume.
- The density of the solution is 0.96 g/mL.
- We will consider a total volume of 100 mL of the solution for easier calculations.

### Step 2: Calculate the Volume of Ethanol and Water
Since the solution is 20% ethanol by volume:
- Volume of ethanol (C₂H₅OH) = 20 mL
- Volume of water (H₂O) = 100 mL - 20 mL = 80 mL

### Step 3: Calculate the Mass of the Solution
Using the density of the solution:
- Mass of the solution = Density × Volume
- Mass of the solution = 0.96 g/mL × 100 mL = 96 g

### Step 4: Calculate the Mass of Water
Since the density of water is approximately 1 g/mL:
- Mass of water = Volume × Density = 80 mL × 1 g/mL = 80 g

### Step 5: Calculate the Mass of Ethanol
Using the mass of the solution and the mass of water:
- Mass of ethanol = Mass of solution - Mass of water
- Mass of ethanol = 96 g - 80 g = 16 g

### Step 6: Calculate the Molar Mass of Ethanol
The molar mass of ethanol (C₂H₅OH) is calculated as follows:
- Molar mass = (2 × 12) + (6 × 1) + (16) = 46 g/mol

### Step 7: Calculate Moles of Ethanol
Using the mass of ethanol:
- Moles of ethanol = Mass / Molar mass
- Moles of ethanol = 16 g / 46 g/mol = 0.3478 mol

### Step 8: Calculate Molarity
Molarity (M) is defined as moles of solute per liter of solution:
- Molarity = Moles of ethanol / Volume of solution in liters
- Molarity = 0.3478 mol / 0.1 L = 3.478 M

### Step 9: Calculate Molality
Molality (m) is defined as moles of solute per kilogram of solvent (water):
- Mass of water in kg = 80 g / 1000 = 0.08 kg
- Molality = Moles of ethanol / Mass of water in kg
- Molality = 0.3478 mol / 0.08 kg = 4.3475 m

### Final Results
- Molarity of the solution = 3.478 M
- Molality of the solution = 4.3475 m